1.The response time is the speed of page downloads and it is critical for a mobile Web site. As theresponse time increases, customers become more frustrated and potentially abandon the site for acompetitive one.Let X = the number of bars of service and Y = response time (to the nearest second)We define the range of the random variables (X, Y) to be the set of points (x, y) in two-dimensionalspace for which the probability that X = x and Y = y is positive.y = Response Time(nearest second)4321Marginal Probability ofDistribution of Xx = Number of Bars of SignalStrength10.150.020.020.0120.10.10.03 0.20.0230.050.05-©xy = E[(X − #x)(Y → Hy)]0.25Marginal Probabilityof Distribution of Ya) Calculate P(Y = 4 | X = 2)b) In one sentence, interpret the result you obtained in (c) above.c) Calculate the Cov( X,Y) using the formula1

Y X Marginal Probability distribution of X 1 2 3 4 0.15 0.1 0.05 3 0.02 0.1 0.05 2 0.02…

Answered: 1. The response time is the speed of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X and Y be independent discrete random variables and suppose that X+Y=2. Show that X and Y are constant random variables.
Exercise 4. Let = {a,b,c,d} and define a probability measure on 222 by P(a) = P(c) = 1/6 and P(b) = P(d) = 1/3. Define random variables X and Y by X(a) = X(b) = 2, X(c) = X(d) = −2 Y(a) = Y(d) = -1, Y(b) = Y(c) = 1. (a) List all sets in σ(Y). (b) Let Z = E(XY), determine Z(a) Z(b), Z(c) and Z(d).
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CHAPTER 5 TEXTBOOK Section 5.18- Exercise 20 Let X be the number of bacterial colonies per cubic centimeter, a Poisson random variable with expected value 3. (i) What is the probability that there is at least one bacterial colony in a randomly chosen cubic centimeter? (ii) What is the probability that in five randomly chosen cubic centimeters there is at least one cubic centimeter where there is at least one bacterial colony? (iii) How many cubic centimeters must be observed for the probability of observing at least one with at least one bacterial colony to be 0.95? 0.9999997 ÷ What is the probability that there is at least one bacterial colony in a randomly chosen cubic centimeter? What is the probability that in five randomly chosen cubic centimeters there is at least one cubic centimeter where 0.9502 there is at least one bacterial colony? How many cubic centimeters must be observed for the probability of observing at least one with at least one 1 bacterial colony to be 0.95?
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